Jarek Rossignac
نویسنده
چکیده
This chapter reviews basic notions of 2D geometry. We start with the study of vectors and points. Then we discuss coordinate systems (frames) and transformations. Finally, we look at lines, edges, triangles, and circles. 1.1 Why are points and vectors important Points and vectors are the fundamental primitives from which most of the representations and of the geometry processing techniques used in Geometric and Visual Computing (GVC) are constructed. Other geometric primitives are often defined and represented using points, vectors, and scalar values representing various measures (angles, distances). For example, a sphere may be represented by its center (point) and by a radius; a triangle is usually defined by its three vertices (points); a ray traced by a photon in the absence of obstacles is conveniently specified by a starting point (maybe the light source) and a travel direction (vector). Hence, much of the geometric processing performed in GVC deals with points and vectors.
منابع مشابه
Grow & Fold: Compression of Tetrahedral Meshes Sm99-021
1 Abstract Standard representations of irregular nite element meshes combine vertex data sample coordinates and node values and connectivity tetrahedron-vertex incidence. Connectivity speciies how the samples should be interpolated. It may beencoded for each tetrahedron as four vertex-references,
متن کاملPhotoMeter: Easy-to-use MonoGraphoMetrics
MonoGraphoMetrics is the science of computing 3D measures from a single image. Several recent research activities have produced theoretical principles and practical tools for extracting 3D measures from uncalibrated photographs. These tools require that the user identifies configurations of edges, which are used to establish constraints or to identify planes in the scene. The process involved i...
متن کاملScrewBender: Polyscrew Subdivision for Smoothing Interpolating Motions
An ordered series of control poses may be interpolated by a polyscrew rigid body motion composed of a series of screws, each interpolating a pair of consecutive control poses. The trajectory of each point during screw motion is (C∞). Although a polyscrew is continuous, velocities are typically discontinuous at control poses when the motion switches between screws. We obtain a smooth motion by s...
متن کامل